IJPAM: Volume 84, No. 2 (2013)

LINEAR INDEPENDENCE OF A FINITE SET OF
DILATIONS BY A ONE-PARAMETER MATRIX LIE GROUP

David Ferrone1, Vignon Oussa2
1Department of Mathematics
University of Connecticut
Storrs-Mansfield, CT 06269, USA
2Department of Mathematics & Computer Science
Bridgewater State University
Bridgewater, MA 02325, USA


Abstract. Let G={etA : t ∈ R} be a closed one-parameter subgroup of the general linear group of matrices of order n acting on Rn by matrix-vector multiplication. We assume that all eigenvalues of A are rationally related. We study conditions for which the set {f(et1A)... f(etmA)} is linearly dependent in Lp(Rn) with 1≤ p< ∞.

Received: October 20, 2012

AMS Subject Classification: 39B52

Key Words and Phrases: orbit, one-parameter, groups, cross-sections, dilation equation

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DOI: 10.12732/ijpam.v84i2.4 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 84
Issue: 2